Common Values of Generalized Fibonacci and Leonardo Sequences
Bibhu Prasad Tripathy and Bijan Kumar Patel
Department of Mathematics
School of Applied Sciences
KIIT University Bhubaneswar
Odisha 751024
India
Abstract:
For an integer k ≥ 2, let
Fn(k)
be the k-generalized Fibonacci
sequence that starts n with 0,..., 0, 1, 1 (k terms)
and each term
afterwards is the sum of k preceding terms. In this paper, we find all
the k-generalized Fibonacci numbers that are Leonardo numbers. More
explicitly, we solve the Diophantine equation
Fn(k) = Lem
in positive integers n, k, m with k ≥ 2.
Full version: pdf,
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(Concerned with sequences
A000032
A000045
A001595.)
Received January 31 2023;
revised versions received February 8 2023; May 17 2023; May 26 2023.
Published in Journal of Integer Sequences,
June 12 2023.
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